Conservative weakly compressible smoothed particle hydrodynamics applied to flows with high vorticity

Abstract

The Smoothed Particle Hydrodynamics (SPH) method in the so-called weakly compressible variant (which mimics the incompressibility conditions) is studied in the context of its resolving power of vortical flows. It is well known that the conservative formulations of SPH have serious problems to provide reasonably accurate solutions even in simple flow cases. This deficiency is additionally emphasized by the fact that conservative SPH formulations are not numerically convergent. We investigate and discuss chosen techniques to improve the results; yet, the convergence issue remains. Maintaining the conservative properties (often presented in the literature as the SPH biggest advantage) requires procedures which are in contradiction with the accuracy improvements. Some myths about SPH are discussed and denied.